in this video I'll be helping you with the Alex problem type called trigonometric functions and special angles problem type one radians we're asked here to find the exact value of cine 3 Pi 4S and for any of the special angles I like to think back to our unit circle put in all the special angles and their values for Quadrant 1 and then use quadrant 1 to find any of the special angles that fall into other quadrants so I'll start by labeling our axes here in radians as zero radians Pi is halfway around the circle so Pi Hales is in the middle and then the multiples of Pi 4S are special angles as well as the multiples of Pi 6 which includes 2 pi 6 which is pi/3 so these are all of our special angles in quadrant 1 and the values starting at zero this is a unit circle so one unit is our x value so this would be 1 Z and then as we've discussed in other videos the pattern is about square roots over two so thinking of one as theare < TK of 4/ 2 next would be theare root of 3/ 2 then the square < TK of 2 over 2 then the square < TK of 1 / 2 is just 12 and the square < TK of 0/ 2 is 0 following the opposite pattern for our y values we started with 0 which was the square < TK of 0/ 2 then the square < TK of 1 / 2 is 12 the square < TK of 2 over 2 the the < TK of 3 / 2 and then the < TK of 4/2 is just 1 so at this point we have all of our special angle cosine and S values our x's and y's here in blue and I can look back and I see that for this question we're looking at 3 Pi 4S so this is a multiple of Pi 4S 3 pi4 would be here which looking back at quadrant one I can see is symmetric to Pi 4S but since we're in quadrant 2 this x value is going to be NE < TK 2 /2 the Y value will be the same as in quadrant 1 the < TK of 2 over2 from here I can look back we were asked for the cosine and cosine is our x value so the cosine of 3 piun 4S is < TK 2 / 2 as the exact value